Find the next three terms.

-1, 2, -4, 8, -16

This is a geometric sequence, that is, a sequence where each successive integer is a result of multiplying the previous one by a fixed, non-zero number called the common ratio.  We need to find which number is the common ratio and then complete the next three terms using that ratio.  If we look at the first and second numbers, we need to ask "what can we multiply by -1 to get 2".  If it's not obvious to you, try looking at the next two numbers... what can you multiply by 2 to get -4.  The answer is -2.

 -1 x -2 = 2
2 x -2 = -4
-4 x -2 = 8
etc...

So we need to go to the end of the sequence and find the next three numbers...

-16 x -2 = 32
32 x -2 = -64
-64 x -2 = 128

Next three numbers in the sequence are 32, -64, 128